已知函数f(x)=√3sin(2x+φ),若f(a)=√3,则f(a+5π/6)与f(a+π/12)的大小关系是?

Question

已知函数f(x)=√3sin(2x+φ),若f(a)=√3,则f(a+5π/6)与f(a+π/12)的大小关系是?

Answer 1

f(a+5π/6)-f(a+π/12)=√3(sin(2a+10π/6+φ)-sin(2a+π/6+φ))
=√3(-sin(2a+2π/3+φ)-sin(2a+π/6+φ))=-√3(sin(2a+2π/3+φ)+sin(2a+π/6+φ))
=-√3(sin(a+5π/12+φ)cos(π/4)